Okay, I've gone through all the work of checking if this actually works as a bomb tester. What I found is that you can use the camera to remove more dud bombs than live bombs, but it does worse than the trivial bomb tester.

So I was wrong when I said you could use it as a drop-in replacement. You have to be aware that you're getting less evidence per trial, and so the tradeoffs for doing another pass are higher (since you lose half of the good bombs with every pass with both the camera and the trivial bomb tester; better bomb testers can lose fewer bombs per pass). But it can be repurposed into a bomb tester.

I do still think that understanding the bomb tester is a stepping stone towards understanding the camera.

Anyways, on to the clunky analysis.

Here's the (simpler version of the) interferometer diagram from the paper:

Here's my interpretation of the state progression:

• Start

    |green on left-toward-BS1>
  

• Beam splitter is hit. s = sqrt(2)

    |green on a>/s + i |green on left-downward-path>/s
  

• non-linear crystal 1 is hit, splits green into (red + yellow) / s

    |red on a>/2 + |yellow on a>/2 + i |green on left-downward-path>/s
  

• hit frequency-specific-mirror D1 and bottom-left mirror

    i |red on d>/s^2 + |yellow on c>/s^2 - |green on b>/s
  

• interaction with O, which is either a detector or nothing at all

    i |red on d>|O yes>/s^2 + |yellow on c>|O no>/s^2 - |green on b>|O no>/s
  

• hit frequency-specific-mirror D2, and top-right mirror

    -|red on b>|O yes>/s^2 + i |yellow on right-toward-BS2>|O no>/s^2 - |green on b>|O no>/s
  

• hit non-linear crystal 2, which acts like NL1 for green but also splits red into red-yellow. Not sure how this one is unitary... probably a green -> [1, 1] while red -> [1, -1] thing so that's what I'll do:

    -|red on f>|O yes>/s^3 + |yellow on e>|O yes>/s^3 + i |yellow on right-toward-BS2>|O no>/s^2 - |red on f>|O no>/s^2 - |yellow on e>|O no>/s^2
  

• red is reflected away; call those "away" and stop caring about color:

    |e>|O yes>/s^3 + i |right-toward-BS2>|O no>/2 - |e>|O no>/2 - |away>|O yes>/s^3 - |away>|O no>/s^2
  

• yellows go through the beam splitter, only interferes when O-ness agrees.

    |h>|O yes>/s^4 + i|g>|O yes>/s^4 + i |g>|O no>/s^3 - |h>|O no>/s^3 - |h>|O no>/s^3 - i|g>|O no>/s^3 - |away>|O yes>/s^3 - |away>|O no>/s^2
  
    |h>|O yes>/s^4 + i|g>|O yes>/s^4 - |h>|O no>/s - |away>|O yes>/s^3 - |away>|O no>/s^2
  
    ~ 6% h yes, 6% g yes, 50% h no, 13% away yes, 25% away no
  

CONDITIONAL upon O not having been present, |O yes> is equal to |O no> and there's more interference before going to percentages:

    |h>/s^4 + i|g>/s^4 - |h>/s - |away>/s^3 - |away>/s^2

    |h>(1/s^4-1/s) + i|g>/s^4 - |away>(1/s^2 + 1/s^3)

    ~ 21% h, 6% g, 73% away

Ignoring the fact that I probably made a half-dozen repairable sign errors, what happens if we use this as a bomb tester on 200 bombs where a hundred of them are live but we don't know which? Approximately:

• 6 exploded bombs that triggered h
• 21 dud bombs that triggered h
• 50 live bombs that triggered h
• 6 exploded bombs that triggered g
• 6 dud bombs that triggered g
• 0 live bombs that triggered g
• 13 exploded bombs that triggered nothing
• 25 live bombs that triggered nothing
• 73 dud bombs that triggered nothing

So, of the bombs that triggered h but did not explode, 50/71 are live. Of the bombs that triggered g but did not explode, none are live. Of the bombs that triggered nothing but did not explode, 25/98 are live.

If we keep only the bombs that triggered h, we have raised our proportion of good unexploded bombs from 50% to 70%. In doing so, we lost half of the good bombs. We can repeat the test again to gain more evidence, and each time we'll lose half the good bombs, but we'll lose proportionally more of the dud bombs.

Therefore the camera works as a bomb tester.